This paper focuses on the time-varying distributed optimization problem (DOP) for multi-agent systems (MASs) in predefined time over an undirected graph, where inequality constraints and external disturbances are introduced in system models. First, a novel result with respect to the stability in predefined time is developed for nonlinear systems by adapting hyperbolic function, where the settling time could be preset freely by users. Second, a piecewise distributed sliding-mode control protocol, which consists of hyperbolic function and barrier penalty function, is designed by doing the segmentation for the time interval on the predefined time. Under the proposed control protocol, the states of all agents are driven to the designed sliding-mode surface, and realize the consensus in predefined time. Moreover, the consensus state converges to the optimal solution of DOP in predefined time. Finally, the effectiveness of the proposed optimization control protocol is verified by applying a simulation example.
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